# Calculation of Comprehensive Ecological Flow with Weighted Multiple Methods Considering Hydrological Alteration

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}with an elongated shape. The average basin length is about 270 km, and the average width is about 90 km. The ratio of length to width is 3:1. The Naolihe basin lies in the temperate continental monsoon climate zone. The multiyear average precipitation is 545 mm, and 70% of the precipitation is mostly concentrated in June, July, August, and September. Moreover, the precipitation in July and August accounts for about 44% of the total. The precipitation in May and June only accounts for 23%.

^{2}. The Caizuizi hydrological station is located at the trunk stream of Naolihe River, in the town of Sanlitun, and has a control area of 20,896 km

^{2}. The Baoan hydrological station is located in the town of Youyi, having a drainage area of 1344 km

^{2}. The Hongqiling hydrological station is located on the Hongqiling farm. Its drainage area is 1147 km

^{2}. Two leading reservoirs are found in the Naolihe basin: the Longtouqiao Reservoir and the Hamatong Reservoir, shown in Figure 1. The first reclamation in the Naolihe basin began in 1956, and no agricultural activities were performed in the study area prior to 1956. Therefore, 1956 was chosen as the start year for this study. The historical daily flow data, except for December to March in the next year due to the freezing period, is from 1956 to 2012 for the four hydrological stations in the Naolihe Basin for this study. Location of the study area is shown in Figure 1.

#### 2.2. Methodology

#### 2.2.1. Evaluation of the Intra-Annual Runoff Distribution Degrees of Evenness

- (1)
- Group and sort historical monthly flow data. Divide the 12 monthly flows in the ith year into a group, and sort the monthly flows into a group in ascending order. The ascending runoff series of the ith year is $\{{r}_{i1},{r}_{i2},\dots ,{r}_{i12}\}$, where i represents the ith year, ${r}_{i1}<{r}_{i2}<\dots <{r}_{i12}$.
- (2)
- Accumulate the ascending runoff data in each group:$${R}_{ik}={\displaystyle \sum _{j=1}^{k}{r}_{ij}(k=1,2,\dots ,12)}$$
- (3)
- Draw a Lorenz curve of the annual distribution for monthly flow. Take k/12 as the abscissa, ${R}_{ik}/{R}_{i12}$ as the ordinate, and draw a Lorenz curve of the annual distribution for monthly flow. The Lorenz curve is shown in Figure 3.
- (4)
- The ith year runoff Gini coefficient GI
_{i}is computed as:$$G{I}_{i}={S}_{{A}_{i}}/({S}_{{A}_{i}}+{S}_{{B}_{i}})$$_{Ai}and S_{Bi}are the area acreages of A_{i}and B_{i}, respectively.

#### 2.2.2. Hydrological Alteration Diagnosis System

#### 2.2.3. Ecological Flow Calculation Method

- In the range of the variability approach (RVA) method, ecological flow calculations should consider the hydrological regime. Parameters of the indicators of the hydrologic alteration (IHA) method are all closely related to runoff, and monthly flow influences river-living organisms, soil, etc. Therefore, the RVA analyses the monthly flow frequency distribution of each month and selects the flow corresponding to 25% and 75% in the frequency distribution as the upper and lower limits of the monthly flow, respectively [26]. Ecological flow is calculated as:$${Q}_{ej}={W}_{jRVA}\times {Q}_{ejRVA}+{W}_{jMFM}\times {Q}_{ejMFM}+{W}_{jADMFFM}\times {Q}_{ejADFMMF}$$
- The steps for ecological flow calculation using the monthly frequency method (MFM) are as follows:
- (1)
- Calculate the monthly flow distribution empirical frequency of the jth month.
- (2)
- Select the probability distribution function and draw the monthly flow distribution theoretical frequency curve of the jth month. The Pearson III distribution curve and generalized extreme value (GEV) distribution curve are commonly used. The GEV distribution curve is better fitting with the runoff data [27].
- (3)
- Select the flow corresponding to the maximum frequency in the GEV distribution curve as the ecological flow of the jth month ${Q}_{ejMFM}$ [28].

- The annual daily mean flow frequency method (ADMFFM) assumes that daily flow may appear in a month with a certain probability. The frequency of daily flow in the jth month of the historical runoff series is calculated and the daily flow corresponding to 60% is selected as the ecological flow [24] of the jth month, ${Q}_{ejADMFFM}$. The ecological flow calculated using this method meets the ecological water requirements in different cases.
- In the comprehensive ecological flow calculation method, ecological flow maintains riverine ecological function. Too much or too little will affect the riverine ecosystem. Therefore, the weights of each ecological flow calculation method are used to comprehensively calculate ecological flow. The steps for this method are as follows:
- (1)
- Evaluate ecological flows from RVA, MFM, and ADMFFM, and the comprehensive evaluation values of RVA, MFM, and ADMFFM of the jth month are ${W}_{jRVA}$, ${W}_{jMFM}$ and ${W}_{jADMFFM}$, respectively.
- (2)
- Calculate the comprehensive ecological flow of the jth month as follows:$${Q}_{ej}={W}_{jRVA}\times {Q}_{ejRVA}+{W}_{jMFM}\times {Q}_{ejMFM}+{W}_{jADMFFM}\times {Q}_{ejADFMMF}$$

#### 2.2.4. Weight Calculation of Comprehensive Ecological Flow

- We first determined the deviation rate of monthly flow. The median of the natural daily mean flow series in the jth month of N years was called the standard value. This index is a ratio of ecological flow in the jth month to the standard value. It reflects the deviation degree between the ecological flow and the natural flow in the same period [28,29]. It is computed as follows:
- (1)
- Calculate the natural daily mean flow in the jth month of N years ${Q}_{ij}$, where i is the year, i = 1, 2, …, N; N is equal to the length of the runoff series; and j is the month, j = 1, 2, …, 12;
- (2)
- Sort ${Q}_{ij}$ in the ascending order ${Q}_{1j},{Q}_{2j},\dots ,{Q}_{nj}$, (${Q}_{1j}<{Q}_{2j}<\dots <{Q}_{nj}$, n is the serial order), where the standard value of the jth month is ${Q}_{mid,j}$;
- (3)
- The calculation formula of the deviation rate of the monthly flow is:$${C}_{j}=\frac{{Q}_{e}{}_{j}}{{Q}_{mid,j}}$$
^{3}/s. If the value is close to 1, the calculated flow is approaching the natural flow and the riverine ecosystem is healthy.

- Satisfaction degree of the monthly ecological flow. This a ratio of the days where the natural flow is equal to or greater than the ecological flow to the total number of days in the same month. The formula to calculate the satisfaction of the monthly ecological water requirement is:$${P}_{j}=\frac{{D}_{ej}}{{D}_{j}}=\frac{{\displaystyle \sum _{i=1}^{N}{\displaystyle \sum _{k=1}^{{K}_{num}}{\mathrm{sgn}}_{ijk}}}}{{D}_{j}}$$$${\mathrm{sgn}}_{ijk}=\{\begin{array}{cc}1,& {Q}_{ijk}>{Q}_{ej}\\ 0,& {Q}_{ijk}<{Q}_{ej}\end{array}$$$${D}_{j}=N\times {K}_{num,j}$$
^{3}/s, and ${Q}_{ej}$ is the ecological flow of the jth month in m^{3}/s. The greater the satisfaction degree of the monthly ecological flow, the healthier the riverine ecosystem. - Suitability degree of the monthly ecological flow. The monthly ecological flow discrete coefficient is the sum of the discrete degree between the median and the characteristic extreme value of the ecological flow and natural flow. It reflects the suitability degree between the ecological flow and natural flow in a month.$${F}_{j}{}^{\prime}=(\frac{{Q}_{emid,j}-{Q}_{mid,j}}{{Q}_{mid,j}}{)}^{2}+(\frac{{Q}_{e\mathrm{max},j}-{Q}_{\mathrm{max},j}}{{Q}_{\mathrm{max},j}}{)}^{2}$$The suitability degree of the monthly ecological flow is computed as:$${F}_{j}=1-{F}_{j}{}^{\prime}/10$$This index reflects the degree of suitability between the total ecological flow requirement and the natural flow in a month. When ${F}_{j}$ is 1, the total ecological flow requirement and the natural flow completely match. When ${F}_{j}$ is 0, the flow is completely unsuitable. A discrete coefficient greater than 10 can be considered completely discrete and the value of the discrete coefficient is equal to 10.
- Ecological flow comprehensive evaluation. The above indexes compare the ecological flow and natural flow from different aspects. The deviation rate of the monthly flow evaluates the degree and magnitude of deviation between the ecological flow and natural flow. The satisfaction degree of the monthly ecological flow temporally analyses the degree of satisfaction between the ecological flow and natural flow. The suitability degree of the monthly ecological flow evaluates the degree of suitability between the ecological flow and natural flow in discrete degrees. The above three indexes were synthesized into a comprehensive index ${\alpha}_{j}$ to evaluate ecological flow in the jth month. The formula for calculating ${\alpha}_{j}$ is:$${\alpha}_{j}=\sqrt[3]{{C}_{j}{P}_{j}{F}_{j}}$$
- Weight calculation of the comprehensive ecological flow. The geometric mean method was used to calculate the weights for each ecological flow calculation method result.$${W}_{jRVA}=\frac{{\alpha}_{jRVA}}{{\alpha}_{jRVA}+{\alpha}_{jMFM}+{\alpha}_{jADMFFM}}$$$${W}_{jMFM}=\frac{{\alpha}_{jMFM}}{{\alpha}_{jRVA}+{\alpha}_{jMFM}+{\alpha}_{jADMFFM}}$$$${W}_{jADMFFM}=\frac{{\alpha}_{jADMFFM}}{{\alpha}_{jRVA}+{\alpha}_{jMFM}+{\alpha}_{jADMFFM}}$$

## 3. Results

#### 3.1. Hydrological Alteration Diagnosis System

#### 3.2. Results of Ecological Flow Calculation

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. An Example for GI Value Calculation

Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Monthly mean flow | 0.08 | 0.009 | 0.027 | 18.4 | 37.7 | 27.4 | 89.5 | 60.1 | 47.5 | 18.6 | 6.6 | 0.57 |

**First**, sort the monthly flows into a group in ascending order; the result is listed in column (3) in Table A2.

**Second**, accumulate the ascending monthly flow series by Equation (1); the result is listed in column (4).

**Third**, calculate the runoff cumulative frequency; for example, 0.000117461 = 0.036/306.486; and calculate the time cumulative frequency; for example, 0.166667 = 2/12.

**Fourth**, draw a Lorenz curve with the series in column (5) and (6) in Table A2.

Month | Order | Monthly Flow | Accumulated Value | Runoff Cumulative Frequency | Time Cumulative Frequency |
---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) |

2 | 1 | 0.009 | 0.009 | 0.000002965 | 0.083333 |

3 | 2 | 0.027 | 0.036 | 0.000117461 | 0.166667 |

1 | 3 | 0.08 | 0.116 | 0.000378484 | 0.25 |

12 | 4 | 0.57 | 0.686 | 0.002238275 | 0.333333 |

11 | 5 | 6.6 | 7.286 | 0.023772701 | 0.416667 |

4 | 6 | 18.4 | 25.686 | 0.08380807 | 0.5 |

10 | 7 | 18.6 | 44.286 | 0.144495997 | 0.583333 |

6 | 8 | 27.4 | 71.686 | 0.233896491 | 0.666667 |

5 | 9 | 37.7 | 109.386 | 0.356903741 | 0.75 |

9 | 10 | 47.5 | 156.886 | 0.51188635 | 0.833333 |

8 | 11 | 60.1 | 216.986 | 0.707980136 | 0.916667 |

7 | 12 | 89.5 | 306.486 | 1 | 1 |

**Figure A1.**Lorenz curve of the annual distribution for monthly flow in 1956. Note: ${A}_{i}$ is a region bounded by Lorenz curve and dashed diagonal, ${B}_{i}$ is a region bounded by Lorenz curve and vertical diagonal.

Baoqing | Baoan | Caizuizi | Hongqiling | |
---|---|---|---|---|

1956 | 0.575167 | 0.542804 | 0.465529 | 0.428152 |

1957 | 0.663721 | 0.599417 | 0.562583 | 0.477699 |

1958 | 0.654811 | 0.621435 | 0.5955 | 0.494503 |

1959 | 0.553547 | 0.530033 | 0.65446 | 0.524602 |

1960 | 0.572132 | 0.553499 | 0.437941 | 0.414069 |

1961 | 0.665426 | 0.646424 | 0.43319 | 0.411643 |

1962 | 0.559209 | 0.553148 | 0.496531 | 0.443979 |

1963 | 0.616581 | 0.515054 | 0.352364 | 0.370382 |

1964 | 0.6856 | 0.65623 | 0.630919 | 0.512584 |

1965 | 0.603178 | 0.580838 | 0.377696 | 0.383314 |

1966 | 0.650194 | 0.545597 | 0.43394 | 0.412027 |

1967 | 0.610227 | 0.606012 | 0.713139 | 0.554558 |

1968 | 0.634882 | 0.469468 | 0.54839 | 0.470453 |

1969 | 0.42967 | 0.441901 | 0.348785 | 0.368555 |

1970 | 0.738535 | 0.615852 | 0.686196 | 0.540803 |

1971 | 0.607347 | 0.588313 | 0.469413 | 0.430135 |

1972 | 0.617986 | 0.543292 | 0.564369 | 0.47861 |

1973 | 0.607321 | 0.607421 | 0.375552 | 0.382219 |

1974 | 0.555022 | 0.582396 | 0.287487 | 0.337262 |

1975 | 0.713496 | 0.661335 | 0.71216 | 0.554058 |

1976 | 0.684477 | 0.570556 | 0.713834 | 0.554912 |

1977 | 0.595298 | 0.538128 | 0.83657 | 0.617569 |

1978 | 0.520268 | 0.545812 | 0.636622 | 0.515496 |

1979 | 0.611183 | 0.632446 | 0.61084 | 0.470432 |

1980 | 0.515341 | 0.534083 | 0.627068 | 0.44741 |

1981 | 0.613004 | 0.581639 | 0.597752 | 0.603207 |

1982 | 0.600386 | 0.556539 | 0.759367 | 0.617718 |

1983 | 0.697738 | 0.628078 | 0.655349 | 0.477994 |

1984 | 0.524324 | 0.410819 | 0.480368 | 0.389041 |

1985 | 0.605347 | 0.513835 | 0.584753 | 0.416934 |

1986 | 0.547696 | 0.493103 | 0.681788 | 0.551018 |

1987 | 0.599018 | 0.558052 | 0.476933 | 0.445092 |

1988 | 0.632303 | 0.533406 | 0.635709 | 0.492935 |

1989 | 0.630692 | 0.412365 | 0.714885 | 0.527368 |

1990 | 0.537402 | 0.507299 | 0.587728 | 0.455828 |

1991 | 0.705846 | 0.692314 | 0.561183 | 0.567586 |

1992 | 0.708555 | 0.63015 | 0.744296 | 0.472671 |

1993 | 0.577032 | 0.445792 | 0.624847 | 0.508258 |

1994 | 0.631919 | 0.582762 | 0.600289 | 0.546941 |

1995 | 0.487417 | 0.452052 | 0.668352 | 0.472467 |

1996 | 0.717055 | 0.590542 | 0.719361 | 0.550217 |

1997 | 0.626837 | 0.558618 | 0.6547 | 0.407772 |

1998 | 0.712293 | 0.465754 | 0.721465 | 0.589609 |

1999 | 0.654239 | 0.651277 | 0.697595 | 0.650854 |

2000 | 0.723293 | 0.637565 | 0.667018 | 0.640227 |

2001 | 0.710492 | 0.629317 | 0.704367 | 0.595746 |

2002 | 0.564298 | 0.535856 | 0.554664 | 0.500066 |

2003 | 0.581597 | 0.546915 | 0.630194 | 0.512214 |

2004 | 0.585974 | 0.549713 | 0.630597 | 0.51242 |

2005 | 0.585971 | 0.549178 | 0.736604 | 0.566536 |

2006 | 0.631846 | 0.558946 | 0.637788 | 0.516091 |

2007 | 0.621954 | 0.623716 | 0.722809 | 0.559494 |

2008 | 0.586923 | 0.597498 | 0.738638 | 0.567575 |

2009 | 0.604515 | 0.639023 | 0.71146 | 0.622316 |

2010 | 0.680025 | 0.651626 | 0.793393 | 0.595616 |

2011 | 0.652022 | 0.546681 | 0.692261 | 0.555792 |

2012 | 0.545863 | 0.567307 | 0.683058 | 0.539201 |

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**Figure 3.**Lorenz curve of annual distribution for monthly flow. Note: ${A}_{i}$ is a region bounded by Lorenz curve and dashed diagonal, ${B}_{i}$ is a region bounded by Lorenz curve and vertical diagonal.

**Figure 4.**The values and their moving average of the Gini coefficient (GI) from 1965 to 2012: (

**a**) Baoqing station, (

**b**) Baoan station, (

**c**) Hongqiling station, and (

**d**) Caizuizi station. Note: 5a moving average is a moving average of 5 years, and 10a moving average is a moving average of 10 years.

**Figure 5.**The mean annual flow from 1965 to 2012: (

**a**) Baoqing station, (

**b**) Baoan station, (

**c**) Hongqiling station, and (

**d**) Caizuizi station. The results of the hydrological alteration diagnosis system show a jump alteration in the GI series in 1966 at the Baoqing station, a trend alteration in 1990 in the GI series at the Baoan station, and jump variations in the GI series in 1987 and 1990 at the Hongqiling and Caizuizi stations, respectively. The alteration in the GI series of the Baoqing station occurred in 1966, and no obvious alteration was perceived in the GI series in the subsequent 46 years. Based on the alteration analysis above, runoff data from 1966 to 2012 were selected as the subsequence to calculate ecological flow at the Baoqing station. Runoff data for the periods 1956–1990, 1956–1987, and 1956–1990 were selected as the subsequence to calculate ecological flow at the Baoan, Hongqiling, and Caizuizi stations, respectively. Results of the hydrological alteration diagnosis system are shown in Table 1.

**Figure 6.**Ecological flow calculation results: (

**a**) Baoqing, (

**b**) Baoan, (

**c**) Hongqiling, and (

**d**) Caizuizi stations.

Diagnosis Method | Intra-Annual Runoff Distribution of GI (1956–2012) | |||||
---|---|---|---|---|---|---|

Station | ||||||

Baoqing | Baoan | Hongqiling | Caizuizi | |||

Primary diagnosis | Hurst coefficient | 0.741 | 0.896 | 0.727 | 0.615 | |

Alteration existence | Yes | Yes | Yes | Yes | ||

Detailed diagnosis | Jump diagnosis | Sliding F test | 1966 (+) | 1990 (+) | 1987 (−) | 1990 (−) |

Sliding T test | 1966 (−) | 1998 (−) | 2009 (−) | 1981 (+) | ||

Lee–Heghinan method | 1966 (+) | 1990 (+) | 1989 (+) | 1990 (+) | ||

Orderly cluster method | 1966 (+) | 1974 (−) | 1987 (+) | 1990 (−) | ||

R/S | 1989 (+) | 1990 (−) | 1979 (−) | 1990 (+) | ||

Brown–Forsythe | 1964(−) | 1990(+) | 1987(+) | 1992 (−) | ||

Sliding run test method | 1992 (+) | 1990 (−) | 1992 (+) | 1985(+) | ||

Sliding rank test method | 1985 (+) | 1992 (+) | 1987 (+) | 1991 (+) | ||

Optimum information dichotomy | 1966 (−) | 1989 (+) | 1989 (−) | 1990 (+) | ||

Mann–Kendall | 1992 (+) | 1992 (−) | 1987 (−) | 1991 (−) | ||

BSYES | 1966 (+) | 1989 (−) | 1987 (+) | 1989 (+) | ||

Trend diagnosis | Trend alteration degree | Significant alteration | Significant alteration | Significant alteration | Significant alteration | |

Correlation coefficient method | (+) | (+) | (+) | (+) | ||

Spearman | (+) | (+) | (−) | (+) | ||

Kendall | (+) | (+) | (+) | (+) | ||

Jump point | 1966 | 1990 | 1987 | 1990 | ||

Jump | Comprehensive weight | 0.55 | 0.67 | 0.42 | 0.34 | |

Comprehensive significance | 4 (+) | 5 (+) | 4 (+) | 4 (+) | ||

Trend | Comprehensive significance | 3 (+) | 3 (+) | 2 (−) | 3 (+) | |

Comprehensive diagnosis | Alteration form selection | Jump efficiency coefficient/% | 45.3 | 35.1 | 52.5 | 50.3 |

Trend efficiency coefficient/% | 38.3 | 46.2 | 39.1 | 37.5 | ||

Diagnosis result | 1966 | 1990 | 1987 | 1990 |

**Table 2.**Ecological flow of the selected series and the whole series in the four stations in the Naolihe basin (m

^{3}/s).

Station | Method | April | May | June | July | ||||

(1) | (2) | (1) | (2) | (1) | (2) | (1) | (2) | ||

Baoqing | RVA | 10.05 | 6.89 | 15.81 | 11.48 | 5.67 | 6.80 | 2.29 | 1.28 |

MFM | 11.19 | 6.85 | 17.99 | 12.85 | 11.95 | 7.72 | 7.39 | 4.95 | |

ADMFFM | 7.64 | 5.90 | 16.84 | 12.55 | 8.35 | 6.55 | 6.52 | 4.35 | |

Baoan | RVA | 6.95 | 4.92 | 6.98 | 4.94 | 2.61 | 1.12 | 2.68 | 1.15 |

MFM | 4.32 | 3.63 | 8.43 | 6.02 | 6.03 | 4.44 | 4.42 | 3.36 | |

ADMFFM | 5.32 | 4.92 | 6.98 | 5.44 | 2.61 | 2.94 | 2.68 | 2.54 | |

Hongqiling | RVA | 8.26 | 8.61 | 15.11 | 12.53 | 6.61 | 3.35 | 5.69 | 0.75 |

MFM | 10.17 | 9.18 | 16.59 | 12.94 | 5.62 | 5.39 | 5.04 | 3.82 | |

ADMFFM | 7.61 | 7.60 | 14.72 | 11.7 | 8.21 | 6.35 | 6.21 | 4.70 | |

Caizuizi | RVA | 57.08 | 37.18 | 30.13 | 38.18 | 30.10 | 32.47 | 17.44 | 29.62 |

MFM | 35.28 | 34.94 | 62.39 | 55.30 | 43.69 | 39.44 | 33.76 | 30.13 | |

ADMFFM | 42.31 | 38.65 | 67.89 | 56 | 35.74 | 31.85 | 29.32 | 28.3 | |

Station | Method | August | September | October | November | ||||

(1) | (2) | (1) | (2) | (1) | (2) | (1) | (2) | ||

Baoqing | RVA | 12.21 | 5.14 | 7.02 | 3.25 | 1.32 | 0.49 | 2.22 | 0.98 |

MFM | 15.42 | 11.66 | 7.44 | 5.09 | 4.44 | 3.01 | 2.26 | 1.63 | |

ADMFFM | 14.82 | 11.65 | 9.42 | 5.5 | 3.22 | 2.03 | 3.82 | 2.5 | |

Baoan | RVA | 5.89 | 2.97 | 5.81 | 8.3 | 2.16 | 1.46 | 2.13 | 1.45 |

MFM | 8.37 | 6.51 | 4.56 | 4.22 | 3.91 | 3.51 | 2.16 | 2.08 | |

ADMFFM | 5.89 | 5.04 | 5.81 | 5.60 | 2.16 | 2.12 | 2.13 | 1.86 | |

Hongqiling | RVA | 10.26 | 5.27 | 5.49 | 1.37 | 4.35 | 2.67 | 2.46 | 1.03 |

MFM | 9.76 | 9.33 | 4.78 | 5.49 | 4.66 | 4.08 | 2.22 | 2.41 | |

ADMFFM | 12.63 | 11.75 | 6.34 | 5.75 | 3.92 | 3.90 | 3.12 | 2.55 | |

Caizuizi | RVA | 17.36 | 35.66 | 15.91 | 26.41 | 15.18 | 19.09 | 33.42 | 19.10 |

MFM | 33.99 | 33.05 | 31.41 | 28.60 | 29.11 | 26.61 | 19.49 | 20.74 | |

ADMFFM | 39.45 | 37.8 | 21.22 | 22.05 | 19.41 | 22.35 | 23.33 | 22 |

**Table 3.**Weights of ecological flow calculated by RVA, MFM, and ADMFFM based on the subsequence series and the entire series, respectively.

Station | Method | April | May | June | July | ||||

(1) | (2) | (1) | (2) | (1) | (2) | (1) | (2) | ||

Baoqing | RVA | 0.31 | 0.29 | 0.44 | 0.32 | 0.44 | 0.31 | 0.42 | 0.32 |

MFM | 0.25 | 0.35 | 0.32 | 0.43 | 0.30 | 0.40 | 0.24 | 0.42 | |

ADMFFM | 0.44 | 0.29 | 0.24 | 0.32 | 0.26 | 0.31 | 0.34 | 0.31 | |

Baoan | RVA | 0.32 | 0.34 | 0.41 | 0.38 | 0.39 | 0.41 | 0.31 | 0.36 |

MFM | 0.29 | 0.34 | 0.35 | 0.39 | 0.17 | 0.43 | 0.41 | 0.39 | |

ADMFFM | 0.39 | 0.35 | 0.24 | 0.39 | 0.44 | 0.43 | 0.28 | 0.35 | |

Hongqiling | RVA | 0.31 | 0.34 | 0.34 | 0.42 | 0.29 | 0.39 | 0.31 | 0.36 |

MFM | 0.27 | 0.33 | 0.33 | 0.42 | 0.29 | 0.42 | 0.29 | 0.38 | |

ADMFFM | 0.42 | 0.29 | 0.33 | 0.32 | 0.42 | 0.31 | 0.40 | 0.30 | |

Caizuizi | RVA | 0.34 | 0.34 | 0.42 | 0.39 | 0.31 | 0.46 | 0.38 | 0.38 |

MFM | 0.37 | 0.35 | 0.22 | 0.34 | 0.24 | 0.44 | 0.24 | 0.37 | |

ADMFFM | 0.29 | 0.36 | 0.36 | 0.35 | 0.45 | 0.46 | 0.38 | 0.40 | |

Station | Method | August | September | October | November | ||||

(1) | (2) | (1) | (2) | (1) | (2) | (1) | (2) | ||

Baoqing | RVA | 0.34 | 0.29 | 0.41 | 0.30 | 0.32 | 0.31 | 0.43 | 0.32 |

MFM | 0.42 | 0.40 | 0.23 | 0.39 | 0.25 | 0.42 | 0.27 | 0.43 | |

ADMFFM | 0.24 | 0.30 | 0.36 | 0.30 | 0.43 | 0.31 | 0.30 | 0.33 | |

Baoan | RVA | 0.43 | 0.41 | 0.18 | 0.40 | 0.29 | 0.37 | 0.29 | 0.41 |

MFM | 0.31 | 0.37 | 0.41 | 0.42 | 0.41 | 0.41 | 0.42 | 0.43 | |

ADMFFM | 0.26 | 0.38 | 0.41 | 0.41 | 0.30 | 0.39 | 0.29 | 0.43 | |

Hongqiling | RVA | 0.25 | 0.42 | 0.20 | 0.39 | 0.30 | 0.42 | 0.25 | 0.33 |

MFM | 0.42 | 0.42 | 0.43 | 0.42 | 0.41 | 0.43 | 0.33 | 0.34 | |

ADMFFM | 0.33 | 0.31 | 0.37 | 0.31 | 0.29 | 0.31 | 0.42 | 0.30 | |

Caizuizi | RVA | 0.40 | 0.39 | 0.24 | 0.33 | 0.29 | 0.38 | 0.23 | 0.31 |

MFM | 0.40 | 0.36 | 0.41 | 0.37 | 0.30 | 0.37 | 0.37 | 0.33 | |

ADMFFM | 0.20 | 0.37 | 0.35 | 0.36 | 0.41 | 0.40 | 0.40 | 0.38 |

Month | Baoqing | Baoan | Hongqiling | Caizuizi | ||||
---|---|---|---|---|---|---|---|---|

(1) | (2) | (1) | (2) | (1) | (2) | (1) | (2) | |

4 | 27.26 | 16.89 | 16.14 | 14.67 | 25.86 | 14.57 | 18.12 | 14.61 |

5 | 14.63 | 19.35 | 12.23 | 16.57 | 32.43 | 28.07 | 21.86 | 12.87 |

6 | 16.15 | 17.29 | 14.97 | 16.12 | 24.79 | 34.65 | 23.44 | 35.32 |

7 | 15.89 | 16.23 | 14.03 | 23.87 | 24.68 | 33.74 | 24.34 | 33.47 |

8 | 19.55 | 24.56 | 18.10 | 22.48 | 27.65 | 32.80 | 22.80 | 23.49 |

9 | 12.56 | 18.96 | 19.57 | 23.63 | 30.08 | 36.36 | 21.42 | 26.31 |

10 | 28.65 | 16.23 | 12.18 | 14.35 | 26.79 | 13.57 | 22.62 | 14.06 |

11 | 28.63 | 15.99 | 12.70 | 14.30 | 16.36 | 14.73 | 15.98 | 13.04 |

Average | 20.42 | 18.19 | 14.99 | 18.25 | 26.08 | 26.06 | 21.32 | 21.65 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xing, Z.; Wang, Y.; Gong, X.; Wu, J.; Ji, Y.; Fu, Q.
Calculation of Comprehensive Ecological Flow with Weighted Multiple Methods Considering Hydrological Alteration. *Water* **2018**, *10*, 1212.
https://doi.org/10.3390/w10091212

**AMA Style**

Xing Z, Wang Y, Gong X, Wu J, Ji Y, Fu Q.
Calculation of Comprehensive Ecological Flow with Weighted Multiple Methods Considering Hydrological Alteration. *Water*. 2018; 10(9):1212.
https://doi.org/10.3390/w10091212

**Chicago/Turabian Style**

Xing, Zhenxiang, Yinan Wang, Xinglong Gong, Jingyan Wu, Yi Ji, and Qiang Fu.
2018. "Calculation of Comprehensive Ecological Flow with Weighted Multiple Methods Considering Hydrological Alteration" *Water* 10, no. 9: 1212.
https://doi.org/10.3390/w10091212